As someone else pointed out below, not all insurance would disappear, just health insurance. About 460,000 people work in health insurance. Even with a single payer healthcare system, some people would most likely still pay for private health insurance, so not all those jobs would be lost. But you are correct, it is going to cost jobs. Same as it will if we ever cut back the size of the military to a more reasonable level. Same as it will for any kind of cost cutting measure. We probably wouldn't want to make this transition in the heart of a recession, but right now would actually be a great time with current employment as strong as it is.
As for property taxes, that is a local government issue. However, considering that property taxes are used to fund local services such as fire departments and police forces, it makes sense to me that there should be some level of taxation. Taxes are just part of being able to enjoy modern, civilized society.
As for cost of education, there are several facets. First, there is the issue of tuition. There are two primary drivers for this. One is the cost of administration, which is ballooning out of control because Americans are so distrusting of government. They are so afraid that faculty are just sitting in their ivory towers pondering the stars, and not providing good education, that we've developed these huge bureaucracies tasked with quantifying the quality of education. This has led to private, for profit education companies like Pearson that try to keep education dependent on their services. They push for ever stricter accreditation requirements for measuring that quality to try to drive universities to depend on these services. In addition to the growing number of administrators required to handle this extra load, the salaries of administrators have been ballooning as well.
The second issue contributing to rising tuition costs is a decrease in state funding. Across the nation, since about the 80's the percentage of a states budget appropriated for higher education has been steadily declining. It has made some moderate gains in many states since the recession, but is nowhere near where it once was.
Finally, there are housing costs. This part is a challenge to address, because on the one hand you have people griping about the costs of university housing being out of control because of luxurious dorm rooms with all the amenities. On the other hand, you have the issue that when schools build basic, no frills dorms as affordable housing options, they can't fill them.